As a passionate advocate of observation based statistical inference in the first third of the 20th century R. A. Fisher introduced the concepts of sufficient statistics, as well as a measure of information, which is invariant with respect to them [1]}. This Fisher information encouraged S. Kullback and R. A. Leibler in the mid-20th century to further investigations, regarding the correspondence between statistics and the uprising information theory of C. E. Shannon [2]}. In the course of their analysis a further invariant structure became apparent, which became known as the Kullback-Leibler divergence [3]}. Although this structure permitted to quantify invariance properties, it did not provide a generic framework, which motivated the incorporation of reversible Markov processes and further statistical divergence functions [4]}, [5]}. A generic theory of equivalence and invariance of statistical models, however, still is missing! A first step in this direction requires to substantiate the objects of desire:
